LDL Solver
Solving a system of linear equations with a quadratic Hermitian positive definite coefficient matrix using the usage of LDL expansion.
blockType: SubSystem
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Path in the library: |
Description
Block LDL Solver solves a system of linear equations usage of LDL decomposition of the input matrix , where
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— square Hermitian positive definite matrix on at the entrance S;
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— matrix of free terms on at the entrance B;
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— solution of a system of equations, a matrix on the output is X.
The algorithm
The LDL decomposition algorithm uniquely represents a Hermitian positive definite input matrix How
Where
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— lower triangular matrix with single diagonal elements (unit triangular matrix);
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— diagonal matrix;
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— Hermitian (complex conjugate) transposed matrix .
The resulting equation will have the form:
When replacing and it turns out one system of equations with a diagonal matrix and two systems of equations with triangular matrices:
Ports
Input
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S
—
matrix of coefficients
matrix M by M
Details
The Matrix in the equation size on . The matrix must be Hermitian positive definite. The block uses only elements of the diagonal and above the main diagonal of the matrix and ignores the rest. Imaginary parts in diagonal elements are ignored. The Inputs S and B must have the same number of lines.
If the input matrix is not positive definite, then the behavior of the block depends on the value of the parameter Non-positive definite input.
| Data types |
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| Complex numbers support |
Yes |
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B
—
the matrix of free terms
matrix M by N | vector M by 1
Details
The Matrix in the equation , given as a matrix of size on or a vector of size on .
If a vector is given on , then the block processes the input vector of length on port B as a matrix on . The Inputs U and B must have the same number of lines.
| Data types |
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| Complex numbers support |
Yes |
Output
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X
—
solving a system of equations
matrix M by N | vector M by 1
Details
The solution of the system of equations returned in the form of a matrix on or vectors on . The size of the output matrix X is the same as the size of the input matrix B.
| Data types |
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| Complex numbers support |
Yes |
Parameters
Main group
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Non-positive definite input —
block behavior if the input matrix is not positive definite
Ignore | Warning | Error
Details
Specify the behavior of the block in case the input matrix is not positive definite:
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Ignore— the unit continues calculations and does not issue a warning. The result is not the right solution. -
Warning— the block continues calculations, but in the command window Engee A warning message is displayed. The result is not the right solution. -
Error— the error dialog box is displayed and the calculations are stopped.
Parameter Non-positive definite input it is diagnostic. Like all diagnostic parameters, it is set to Ignore in the code generated for this block by the code generator.
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| Values |
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| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |